Simplify (7x)^9/(7x): Applying Exponent Division Rules

To solve the expression $\frac{(7\times x)^9}{(7\times x)}$, we can utilize the Power of a Quotient Rule for exponents. According to this rule, for any non-zero number $a$ and integers $m$ and $n$, the expression $\frac{a^m}{a^n}$ can be simplified to $a^{m-n}$.

Applying this rule, we identify the base $(7\times x)$ as the variable and analyze the exponents:

• The numerator is $(7\times x)^9$, which means the power 9 applies to the term $(7\times x)$.
• The denominator is $(7\times x)^1$, which implies a power of 1.

Now, we apply the quotient rule:

$\frac{(7\times x)^9}{(7\times x)} = (7\times x)^{9-1} = (7\times x)^8$

Thus, the expression simplifies to $(7\times x)^8$. This is achieved by subtracting the exponent in the denominator from the exponent in the numerator.

The solution to the question is: $(7\times x)^8$.